An educational researcher wishes to know if there is a difference in academic performance for college freshmen that live on campus and those that commute. Data was collected from 220 students. Can we conclude that freshman housing location and academic performance are related? Location Average Below Average Above Average Total
On campus 77 37 41 155
Off campus 28 12 12 52
Total 105 49 53 207
a) Find the value of the test statistic. Round your answer to three decimal places.
b) Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.
c) State the conclusion of the hypothesis test at the 0.05 level of significance.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation:

figure c

step-by-step explanation:

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